Andrews-Curtis Conjecture
Problem
The Bradley BEAR group that I am involved in is looking to prove/disprove the following concept.
Definitions
Alphabet: X={x1, x2,…, xn}
Syllables: x1±1, x2±1,…, xn±1
Words: Strings of syllables
Ex: x1 x2 x1-1 x5
Syllables are words of length one.
The (unique) word of length zero is denoted *.
Words are multiplied by using concatenation (and reduction)
Ex:
w1 = x1 x3 x2-1
w2 = x2 [...]